A351424 a(n) = n! * [x^n] -log(1 - f^(n-1)(x)), where f(x) = log(1+x).

1, 0, 3, -48, 1270, -50375, 2803829, -208616562, 20003317746, -2402323535658, 353219463307920, -62411008199372327, 13048469028962425266, -3186116313706825820802, 898478811755719496052919, -289795933163271680910773018, 106008143082108931457543700504

Offset: 1

Author

Seiichi Manyama, Feb 11 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..247

Crossrefs

Main diagonal of A351420.

Cf. A139383, A302358, A351433.

Programs

Maple

g:= x-> log(1+x):
a:= n-> n! * coeff(series(-log(1-(g@@(n-1))(x)), x, n+1), x, n):
seq(a(n), n=1..19);  # Alois P. Heinz, Feb 11 2022

Mathematica

T[n_, 1] := (n - 1)!; T[n_, k_] := T[n, k] = Sum[StirlingS1[n, j] * T[j, k - 1], {j, 1, n}]; a[n_] := T[n, n]; Array[a, 16] (* Amiram Eldar, Feb 11 2022 *)

PARI

T(n, k) = if(k==1, (n-1)!, sum(j=1, n, stirling(n, j, 1)*T(j, k-1)));
a(n) = T(n, n);

Formula

a(n) = T(n,n), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.